Some Properties And Application Of Operator Semigroups And Families Of Related Operators

The present thesis is composed of four parts.In the first part, the developing history of the operator semigroups in functional analysis is simply introduced , then we mainly introduce the meaning of the discussed problems and the main contents.In the second part, we consider a repairable maintenance system. By means of the C0 - semigroup theory of bounded linear operators in functional analysis we prove that thissystem has a unique nonnegative solution.In the third part, we introduce integrated semigroups and analytic families of integrated semigroups. The relations between the three natural ways to understand analyticity of the family are clarified. It is the same as the cosine operator.In the forth part, we mainly discuss the properties of cosine operators, such as the normcontinuity, locally Lipschitz continuity, which are preserved under the multiplicative perturbation with the (Z)-condition.